How to conclusively find out if my family has Jewish ancestry?

I’m trying to solve a generational question. Growing up I swear I heard my mother consistently say there were “rumors” of our family being Jewish due to my grandfather keeping at least somewhat kosher, saying what we thought were prayers in Hebrew before he had a trake put in, “looking” Jewish, and having family sent away both by the Nazis and Russians. Given the records of Communist occupation being sealed, I don’t really know the first place to start with regard to finding out if this supposed rumor is true or not. I imagine given all the turmoil Hungary went through hiding out as Christians (if that was even possible post-Horthy) wasn’t that bad of an option if it could be made.

Whether it is or isn’t makes no big difference, its just a curiosity. I grew up around a fairly large NYC area Jewish community but growing up my family went to a non-denominational “We don’t care your faith just come to share a service” Protestant church. At one point we joked the congregation was 70% Catholic.

So, do I call a rabbinim? Do I look up records in the cities where my family has lived? Do I call up my aunt in the village to ask if our gravestones being different from the Russians means anything? Do I take a DNA test? I’m really at a loss. This has puzzled me for the last 8 years, and I’m only reaching out because its late at night and I got a fire under my ass to get something done that isn’t a coding project.